$f(x)$ is twice differentiable polynomial function such that $f(1)=1, f(2)=4, f(3)=9$, then

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Professor PC Thomas Classes · Answer

(d) : Let a function be $g(x)=f(x)-x^{2}$\ $\Rightarrow \quad g(x)$ has at least 3 real roots which are $x$ $=1,2,3$\ $\Rightarrow \quad g^{\prime}(x)$ has at least 2 real roots in $x \in(1,3)$\ $\Rightarrow \quad g^{\prime \prime}(x)$ has at least 1 real root in $x \in(1,3)$\ $\Rightarrow f^{\prime \prime}(x)=2$ for at least 1 real root in $x \in(1,3)$.\